which is one of the most popular measures of distinguishability for quantum
states. In fact, for the single-copy state discrimination (\(M=1\) ) we
have [1]}, [2]}, [3]}, [4]}
\(\frac{1-\sqrt{1-F(\rho _{A},\rho _{B})}}{2}\le P_{e}\le \frac{Q}{2}\le \frac{\sqrt{F(\rho _{A},\rho _{B})}}{2}.\) 
